Quantum Black Holes as Solvents Erik Aurell Krakow Quantum Informatics Seminar (KQIS) March 10, 2020 Erik Aurell, Michał Eckstein, Paweł Horodecki [arXiv:1912.08607] March 10, 2020 Centrum Informatyki AGH 1
Picture of the black hole M87* 11 April 2017 Event Horizon Telescope (EHT) European Southern Observatory (ESO) Wikimedia commons March 10, 2020 Centrum Informatyki AGH 2
Number of outstanding people who have worked on or around quantum black holes is huge Hawking, Bekenstein, Penrose, Zeldovich, Novikov, Wheeler, Zurek, Susskind, Maldacena, Wald, Unruh, ’t Hooft, Verlinde, Verlinde, Giddings, Horodecki, Horodecki, Aaronson, Page, Strominger, Bousso, Harlow, Sorkin, Smolin, Wilczek, Życzkowski,… To give appropriate credit is impossible. March 10, 2020 Centrum Informatyki AGH 3
Bekenstein-Hawking (black hole) entropy Entropy of a black hole of area A: Boltzmann’s constant Newton’s constant Planck’s constant speed of light Entropy of a black hole is equal to ¼ the area measured in the units of Planck area. This entropy is enormously large. More than 99.99999% of all the entropy in the universe today. Most of the slide courtesy Dave Bacon, U Washington March 10, 2020 Centrum Informatyki AGH 4
Black hole information paradox Take a large piece of matter Ways out? in a pure quantum state, and Fundamental information loss : have gravity turned off. actually the dynamics of a quantum Turn on gravity. The matter black hole is not unitary. collapses in a black hole. Physics at horizon : firewalls or other physics stops the collapse. The black hole evaporates through Hawking radiation. Information return in Hawking radiation : entanglement between At the end the black hole is early and late Hawking radiation. gone, and all that remains is thermal radiation. Remnants : evaporation is not complete, something remains that A pure state has developed keeps the information. into a mixed state. This breaks unitarity. The issue is still very actively discussed… March 10, 2020 Centrum Informatyki AGH 5
The entropy of a black hole is much, much larger than the entropy of anything that could have formed the black hole. Even though the black hole has been compressed to a much smaller volume. Normal entropy does not behave that way. March 10, 2020 Centrum Informatyki AGH 6
For a classical liquid this is so. N is the volume of phase space accessible to the molecules of the liquid. Or for the molecules of a salt crystal which dissolves into a liquid like water. The process of solvation proceeds when the dissolving salt molecules gain more entropy in the larger volume than they lose in internal energy by moving away from the salt crystal. What is N for the quantum black hole? Is there even such a thing? For a negative answer, see e.g. Hossenfelder & Smolin, Phys. Rev. D 81: 064009 (2010). On the other hand “…thermodynamics is the only physical theory that will never be over- turned…” demands that if black hole entropy is an entropy in the sense of normal entropy, there must be an N . March 10, 2020 Centrum Informatyki AGH 7
Entanglement entropy von Neumann entropy. The quantum version of Shannon entropy. S cannot increase under local operations and classical communication (LOCC) [Horodecki 4 , Rev Mod Phys (2009)]. Gravitational collapse is a local process (mostly). Entanglement entropy between a black hole and the rest of the universe (ancilla) cannot be much larger than the entanglement entropy of the star that gave rise to the black hole. March 10, 2020 Centrum Informatyki AGH 8
Entanglement with gravity Initial state of the star and ancilla and a pure quantum gravity state (if such a thing exists) Final state of black hole + gravitation with the ancilla An “entangled entanglement” state [Walther, Resch, Brukner & Zeilinger, Phys. Rev. Lett. 97 :020501 (2006)]. Internal B-G entanglement can be much greater than the one between the joint system B+G and rest of the Universe. This can hence be N . March 10, 2020 Centrum Informatyki AGH 9
Table-top experiments An active field with contributions from Brukner. Aspelmeyer, Pikovski, Vedral, Bose, Millburn and others. The experts believe that the quantum nature of gravity can be shown (or disproven) in quantum optics experiments, in a few years’ time. Fig 1 in Belenchia, Wald, Giacomini, Castro-Ruiz, Brukner & Aspelmeyer Phys. Rev. D 98: 126009 (2018) March 10, 2020 Centrum Informatyki AGH 10
“Reasonable ideas” of a quantum black hole It is in a maximally mixed state given its macroscopic parameters (mass, charge, angular momentum) [a microcanonical ensemble] (unclear what this actually means if you don’t know what the quantum states are, but it is an often stated assumption…) A small quantum test particle which is not at the singularity behaves as if it is moving in the background of a classical black hole. Experimentally shown for quantum particles moving in the gravitational field of the Earth [Nesvizhevsky et al, Nature 415 :297299 (2002)] A small quantum test particle also behaves as if moving in the classical background when evolving with a pure quantum state of the black hole picked randomly with respect to the microcanonical ensemble. A kind of typicality argument [Reimann, Phys. Rev. Lett. 101 :190403 (2008); Gogolin & Eisert Rep. Prog. Phys . 79: 056001 (2016)]. March 10, 2020 Centrum Informatyki AGH 11
If the “reasonable ideas” are admitted… It suffices to consider the evolution of a pure state of the test particle and a pure state of the gravitational field of the black hole. ? March 10, 2020 Centrum Informatyki AGH 12
Model for information Suppose all the final states close or at the singularity are very similar. From this does not follow that the final states of the gravitational field are the same. The (classical) action of the two paths which will be arbitrarily different when they hit the singularity (infinite tidal forces). There may also be a quantum information argument based on distinguishability of quantum states (this you have to ask Paweł Horodecki and Michał Eckstein). March 10, 2020 Centrum Informatyki AGH 13
Model of the aftermath Suppose that Hawking radiation is a unitary process. The initial state has no photons in the radiation field: | ۧ 𝑑 𝑗 | ۧ 𝑇 𝑗 | ۧ ⊗ | ۧ Ψ = 𝐻 𝑗 𝑆 0 𝑗 The final state should be an entangled state between radiation and gravitation (the matter of the hole has returned to the vacuum state): Ψ′ = 𝑑′ 𝑘 | ۧ ۧ 𝑆 𝑘 | ۧ | 𝐻 𝑘 In the black hole information paradox context, this is hence a proposal of a remnant, but not of the usual kind. March 10, 2020 Centrum Informatyki AGH 14
Bekenstein 1973:2001 Jacob Bekenstein in 1973 proposed that BH entropy is the log of the number of different quantum systems that could have given rise to the black hole, and estimated that quantity. In 2001 he considered a black hole emitting Hawking radiation and at the same time being feeded by a stream of matter so that its mass, angular momentum and charge stays constant: [The black hole then] does not change in time, and neither does its entropy. But surely the inflowing matter is bringing into the black hole fresh quantum states; yet this is not reflected in a growth of SBH! [...] If we continue thinking of the Hawking radiation as originating outside the horizon, this does not sound possible. Bekenstein, Stud. Hist. Philos. Mod. Phys . 32 :511-524 (2001) From the point of view of today, the above describes a non-equilibrium stationary state (NESS). It could be possible. Compare Earth atmosphere. March 10, 2020 Centrum Informatyki AGH 15
Thanks Michał Eckstein TEAM-NET Kraków Paweł Horodecki ICTQT Gdańsk Pictures / slides from internet ESO Dave Bacon, U Washington March 10, 2020 Centrum Informatyki AGH 16
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